Distortion

The Zeiss lens produces a negligible amount of barrel distortion (~0.2%) which is irrelevant in field conditions.

Vignetting

As a full format lens it has an easy play on micro-4/3 cameras when it comes to vignetting. Even at f/2 it's nothing to worry about in real world situations.

MTF (resolution)

The Zeiss lens delivers an impressive quality from f/2.8 onwards but it struggles a bit at f/2. It has no problems at max. aperture on the Leica M8 but it seems as if it's not aligned to the LiveMOS (4/3) sensor characteristics. That said the center quality is still very good here so it's perfectly usable for e.g. portraits at this setting but at least the corner performance leaves something to be desired. However, there's already a boost in border quality at f/2.8 and from f/4 onwards it's extremely sharp across the frame.

Below is a simplified summary of the formal findings. The chart shows line widths
per picture height (LW/PH) which can be taken as a measure for sharpness.
If you want to know more about the MTF50 figures you may check out the corresponding
Imatest Explanations

Chromatic Aberrations (CAs)

Lateral CAs are very well controlled with an average pixel width of less than 0.9px at the image borders. This isn't really objectionable/visible in field conditions.